International Journal of Structural Stability and Dynamics

The pantograph-catenary system is essential to the operation of modern railways. The overhead catenary system serves to deliver steady electric power to the trains running on the railways. The propagation of waves in the catenary system can be significantly affected by its interaction with the pantograph. To investigate the wave transmission via the contact wires of a catenary system, a simplified model composed of a pre-tensioned wire suspended by periodic spring supports is adopted. For a periodic structure with wider band gaps (or stop bands), a larger cluster of frequencies of the transmitting waves can be filtered out. This is beneficial to the maintenance of the catenary system as unwanted vibrations have been reduced. To widen the band gaps, a resonator can be equipped on each of the spring supports for attenuation of a wider range of transmitting waves in the pre-tensioned wire. In this study, a unit cell conceived as the spring–resonator–wire unit is adopted to formulate the dispersion equation in closed form, from which the critical condition for widening the band gaps is derived. In addition, the moving pantograph is modeled as a moving force. From the exemplar study, it was shown that the installation of proper resonators on a catenary system can increase the gap bandwidth, such that the pantograph-induced wave transmission in the contact wires will be attenuated or filtered out.

A large number of joints that make possible the smooth deployment of an articulated truss may lead to the unexpected variation of the whole dynamic characteristics of the truss. In this paper, attention is focused on exploring the joint characteristics and their effects not strictly following the conventional linear assumption. Particularly, the effects of cubic nonlinear characteristics of joints on the dynamic behavior of articulated trusses are investigated. First, the equivalent dynamic model of the truss cell in the frequency domain is developed for enhancing the computational efficiency. With the employment of the describing function method (DFM), the frequency responses of the planar articulated truss considering the cubic nonlinearity of joints are obtained analytically. Moreover, the transient responses of the articulated truss under external shock loads are obtained numerically. Subsequently, the variations in frequency obtained by the fast Fourier transformation (FFT) of the numerical results show consistent tendency compared with those obtained by the equivalent dynamic model of the planar articulated truss. Finally, several conclusions are presented at the end.

In this paper, we study vibro-acoustic behavior of auxetic sandwich panels subjected to different excitations and boundary conditions. The core of this panel has the auxetic feature (with negative Poisson’s ratio or NPR) with anti-tetrachiral honeycomb structure. Mechanical behavior of the core is formulated using theoretical relations presented for this kind of auxetic. Using the Finite Element Method, the modal analysis and spectral analysis of the structure are accomplished. Different random colored noises are applied as the system excitation. First, a parametric study is performed; and some interesting results are observed from investigating the effects of geometric parameters, boundary conditions, and noise color on the vibro-acoustic behavior of the structure. These parameters affect the natural frequencies, level of radiated sound, and mass of the structure. An optimization algorithm is applied to the geometrical parameters in order to simultaneously reduce the level of radiated sound and preserve the amount of total mass. By the use of the Genetic Algorithm (GA), we could achieve a remarkable noise attenuation gain. It is shown that the GA choses different optimized parameters for the structure according to the location of the load and frequency content of the load spectrum.

Investigated herein is the buckling of Euler–Bernoulli nano-beams made of bi-directional functionally graded material with the method of initial values in the frame of gradient elasticity. Since the transport matrix cannot be calculated analytically, the problem was examined with the help of an approximate transport matrix (matricant). This method can be easily applied with buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on gradient elasticity theory. Basic equations and boundary conditions are derived by using the principle of minimum potential energy. The diagrams and tables of the solutions for different end conditions and various values of the parameters are given and the results are discussed.

For high-rise buildings subjected to ambient excitations such as typhoons and earthquake actions, their structural responses may include non-stationary features. Under such conditions, traditional modal identification methods may not be applicable due to the violation of the stationary assumption of the response signals. To deal with this issue, a novel modal identification method is presented in this paper based on combination of the variational mode decomposition (VMD) and direct interpolation (DI) techniques. Through numerical simulation study of a three-story frame structure, the effectiveness and accuracy of the combined VMD-DI method for modal identification of the structure are validated for the case of the structural responses containing non-stationary properties and high-level noise. Moreover, the novel method is further applied to the field measurements of acceleration responses of a 600m high skyscraper during a typhoon. The identified results verify the applicability and accuracy of the combined VMD-DI method in field measurements. This paper aims to provide an effective tool for modal identification from non-stationary structural responses of high-rise buildings.

This paper describes the issue of validity of running safety criterion on high-speed railways (HSR). In this research, the 2D model of ‘car–track–bridge’ system is used. A feature of HSR is the practical reaching of the critical speeds that cause resonance of bridge superstructures. The Eurocode establishes the limit of bridge superstructure acceleration below 5m/s² in case of nonballasted track. This limit does not suit in certain conditions such as resonance of the superstructure that is permitted in Eurocode. In this case, there is no correlation between acceleration limit and firm wheel–rail contact. The numerical analysis shows repeated wheel lift-off during train passing a bridge zone. It is resonance of the bridge deck that causes this effect because without resonance, the running train is safe. Lower damping in nonballasted track increases resonant vibration influence.

Extreme actions, such as impact loads, contain many uncertainties and hence, may not be analyzed by a deterministic approach. In this paper, an effective framework for performance evaluation of reinforced concrete (RC) beams subjected to impact loadings is proposed. For this purpose, a simple yet effective model considering the shear-flexural interaction is developed based on available impact test results. By incorporating the shear effect, both the maximum displacement and impact force are well predicted, by which the proposed model for the impact analysis of RC beams is validated. The joint probability density function (PDF) of two damage indexes, i.e. local drift ratio and overall support rotation, is used to represent the local shear damage degree and the overall flexural damage degree. Taking advantage of the probabilistic framework and the effective model, reliability analysis of the RC beams under different impact scenarios is performed. The damage, described in this study by the joint PDF, is highly affected by the combination of impact mass and velocity. Thus, the mass–velocity ($m$–$v)$ diagrams for various performance levels are generated for the damage assessment of the RC beams. Furthermore, the contribution of the local and global responses to the failure probability is quantified using the proposed probabilistic framework.

A mathematical model is proposed to analyze the stability of composite shafts, considering the internal damping, transverse shear deformation and Poisson’s coupling effect at the same time. The strain–displacement relations are described using the Timoshenko beam theory, and the strain energy and kinetic energy are expressed using the weak form quadrature element method (QEM), for which each nodal point has 4 degrees of freedom. Then, the motion equation of the system is established using the Lagrange equation. The instability thresholds of the composite shaft are determined using the proposed model. The results were compared with those calculated by the equivalent modulus beam theory (EMBT), equivalent single layer theory (ESLT) and simplified homogenized beam theory (SHBT). Good agreement has been achieved. Therefore, the proposed model can be effectively used for the dynamic analysis of composite shafts.

In this study, the collapse behavior of a family of tensegrity structures, i.e. di-pyramid (DP) barrel-vaults that can offer promising solutions for civil engineering applications is analyzed. Depending on whether struts’ snap or cables’ rupture dictate the occurrence of overall collapse, two different designs are considered. The effects of geometric parameters, self-stress properties, loading type, boundary conditions and strengthening schemes on the structural behavior are discussed. It is found that the structures with symmetric and ridge loading types undergo bifurcation type instability instead of limit point which is encountered in the cases with asymmetric loading type. Constraint against lateral thrust is beneficial in improving strength and initial stiffness of the studied cases, by as much as 60% and 90%, respectively. In most cases, the rate of strength variation associated with increasing self-stress levels is quite slow, while the slackness load increases by at least 400% being the primary achievements. By using non-uniform self-stress distribution, the initial stiffness of these structures can be increased up to 240%. Increasing the rise-to-span ratio improves the initial stiffness and collapse strength of the structure significantly at the expense of expedition of cables slackness. Significant gains in collapse resistance of these structures under symmetric loading are obtained with strengthened critical struts or cables, depending on which collapse case dominates, but the initial stiffness is generally not influenced by these schemes.

In this paper, the semi-active suspension in railway vehicles based on the controlled magnetorheological (MR) fluid dampers is examined, and compared with the semi-active low and semi-active high suspension systems to enhance the running safety and ride quality for a high-speed rail vehicle. Predictive model controllers are used as system controllers to determine the desired damping forces for front and rear bogie frame with force track-ability. A 28 degree of freedom (DoF) mathematical model of the rail vehicle is formulated using nonlinear vehicle suspension and nonlinear heuristic creep model. The MR model of Ali and Ramaswamy is formulated to characterize the behavior of the MR damper. The simulation result is validated using the experimental results. Four different suspension strategies are proposed with MR damper, i.e. passive, semi-active low, semi-active high and semi-active smart controller based on predictive model controller. A comparison indicates that the semi-active controller gives the optimum for comfort vibration actuation and improves the ride quality and it has little influence on derailment quotients, offload factors, as a result, it will not endanger the running safety of rail vehicle.

In this paper, a robust parallel finite-element/genetic-algorithm (FE/GA) procedure is presented for finding the optimal layout of wave barriers in the ground alongside the underground or above-ground railways. The proposed FE/GA procedure is capable of optimizing the topology of the wave barriers by altering the FE model geometry and mesh at each optimization step to cope with the excitations by underground, above-ground, and simultaneous under- and above-ground loadings. The results obtained show that this coupled procedure is effective for the analysis and design of different types of wave barriers subjected to dynamic transient loadings. Three different types of wave barriers are studied including wave impeding blocks (WIBs), jet-grouted columns, and trenches. It is found that the open trenches have the largest mitigation capacity and if they cannot be used, the WIBs perform better than the jet-grouted columns. Although the wave barriers can notably reduce the ground vibrations induced by underground trains, they perform more effectively when the source of vibrations is located at the ground surface.

The main purpose of this paper is to examine the effects of incomplete boundary conditions and actuator delay on the dynamic responses of seismically excited civil structures. A set of constraint equations representing the reserved interface degrees-of-freedom (DOFs) and the delay are introduced to form a mechanical model of real-time hybrid simulation (RTHS) (referred to as RTHS-I&A) for a multi-degree-of-freedom (MDOF) system based on dynamic substructure method (DSM). Then, the RTHS-I&A system is modeled by a discrete closed-loop transfer function based on discrete control theory, using a selected integration algorithm, and the stability of the system is investigated by examining the poles of the function. Three typical cases with different structural properties are utilized to investigate the effects of incomplete boundary conditions and actuator delay. The results show that both incomplete boundary conditions and actuator delay greatly affect the dynamic responses of structures, and the combination of the two factors will amplify their influence especially on the nodes at the interface. The numerical model of RTHS-I&A proposed in this paper is quite useful for evaluating the responses of structures with different interface conditions and loading schemes that are preliminarily designed before a physical testing is conducted, and provides guidance for future relevant researches.

The Bayesian model updating approach (BMUA) has been widely used to update structural parameters using modal measurements because of its powerful ability to handle uncertainties and incomplete data. However, a conventional BMUA is mainly used to update stiffness with the assumption that structural mass is known. Because simultaneously updating stiffness and mass leads to unidentifiable case or coupling effect of stiffness and mass, this assumption in conventional BMUA is questionable to update stiffness when the mass has significantly changed. This study proposes a new updating framework based on two structural systems: original and modified systems. A modified system is created by adding known mass to the original system. Different from the conventional Bayesian approach, two sets of measured vibration data in the proposed Bayesian approach are obtainable to address the coupling effect existing in the conventional Bayesian approach. To this end, a new approach reformulates the prior probability distribution function and the objective function. Two numerical simulations are considered to demonstrate the performance of the proposed approach, including (1) parameter identification, (2) posterior uncertainties, (3) probabilistic damage detections. The proposed BMUA outperforms a conventional BMUA in identifying both stiffness and mass.

In practical civil engineering, structural damage identification is difficult to implement due to the shortage of measured modal information and the influence of noise. Furthermore, typical damage identification methods generally rely on a precise Finite Element (FE) model of the monitored structure. Pointwise mass alterations of the structure can effectively improve the quantity and sensitivity of the measured data, while the data fusion methods can adequately utilize various kinds of data and identification results. This paper proposes a damage identification method that requires only approximate FE models and combines the advantages of pointwise mass additions and data fusion. First, an additional mass is placed at different positions throughout the structure to collect the dynamic response and obtain the corresponding modal information. The resulting relation between natural frequencies and the position of the added mass is sensitive to local damage, and it is thus utilized to form a new objective function based on the modal assurance criterion (MAC) and $l_1$-based sparsity promotion. The proposed objective function is mostly insensitive to global structural parameters, but remains sensitive to local damage. Several approximate FE models are then established and separately used to identify the damage of the structure, and then the Dempster–Shafer method of data fusion is applied to fuse the results from all the approximate models. Finally, fractional data fusion is proposed to combine the results according to the parametric probability distribution of the approximate FE models, which allows the natural weight of each approximate model to be determined for the fusion process. Such an approach circumvents the need for a precise FE model, which is usually not easy to obtain in real application, and thus enhances the practical applicability of the proposed method, while maintaining the damage identification accuracy. The proposed approach is verified numerically and experimentally. Numerical simulations of a simply supported beam and a long-span bridge confirm that it can be used for damage identification, including a single damage and multiple damages, with a high accuracy. Finally, an experiment of a cantilever beam is successfully performed.

In this paper, the buckling characteristic of FGM plate considering the surface effect is studied based on general third-order plate theory and non-local theory. The surface effect of FGM plate is captured by the surface elasticity theory. The Kirchhoff hypothesis is released by employing parabolic variation of transverse shear strains. By using Navier solution technique, analytical solutions of buckling loads of FGM plate with surface effect are given, and detailed parametric studies are presented to show the relationship between surface effects and the plate thickness, power-law index, surface residual stress, surface moduli and non-local parameter. Furthermore, the surface effect on the buckling characteristic of FGM plate is also discussed.

In this paper, a mathematical approach is presented for the forced vibration analysis of a multiple DOF system that is governed by ordinary differential equations with both time-periodic stiffness and external force that have different periods. Based on an equivalent dynamic system, a closed-form solution, i.e. a special trigonometric series, is presented for the forced vibration response of the system. Computation is realized by applying the harmonic balance operation, and the parametric vibration equation is converted into a set of infinite-order linear algebraic equations. Based on the physical property of the forced vibration response, all the coefficient vectors of the forced response are solved by the use of inverse matrix. The present approach can be used to predict the forced vibration response and its spectrum with better computation performance. It can help reveal some nonlinear phenomena in the parametric system. Therefore, it proves to be a useful tool for future research and engineering applications of parametric systems.